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This weekend, the local Cinema sold a total of 8500 movie tickets. The proceeds totaled $64,600. Tickets can be bought in one of 3 ways a matinee ticket costs $5 student tickets costs $6, and regular tickets are $8.50. How many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?​

Answer :

varshamittal029

Number of matinee tickets = 900

Number of student tickets = 1800

Number of regular tickets = 5800

  • Algebra is the branch of mathematics that represents problems and situations in the form of mathematical expressions. It contains variables such as x, y, z, and operations such as addition, subtraction, multiplication, and division to form  meaningful mathematical expressions.

  • Algebra is used mostly in all areas of mathematics like trigonometry, calculus, and coordinate geometry. A simple example of an algebraic expression  is 9x + 4 = 8.

  • Algebra deals with symbols, and these symbols are related to each other by operators. It's not just a mathematical concept, it's a skill that we all use subconsciously in our daily lives.

Let x be the number of matinee tickets.

In that case, the number of  student tickets is 2x.

The number of regular  tickets is (8500-x-2x) = (8500-3x).

Total money

5x + 6*(2x) + 8.50*(8500-3x) = 64600

Simplifying and solving for x

5x + 12x - 8.50*3*x + 8.50*8500  = 64600

5x + 12x - 8.50*3*x = 64600 - 8.50*8500

Solving x , we get

x = 900

Number of matinee tickets = 900

Number of student tickets = 1800

Number of regular tickets = 8500 - (900+1800) = 5800

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